Formal Verification of Cloud Scaling Policies: A Comparative Study using Markov Decision Process and Discrete-Time Markov Chain

Abstract

Cloud scaling plays a critical role in fulfilling the resource requirements of web-based enterprises. Nevertheless, current autoscaler implementations primarily operate reactively, triggering scaling actions based on predetermined thresholds. This approach often leads to erroneous decisions during peak hours, resulting in resource waste, energy consumption, performance degradation, and QoS violations. To overcome these challenges, we propose a formal verification approach utilizing probabilistic model checking, specifically Markov Decision Process (MDP) and discrete-time Markov Chain (DTMC), for analyzing the cloud scaling process. In this investigation, we compare the insights obtained from evaluating MDP and DTMC models for cloud scaling based on four key metrics: latency violation, CPU utilization, response time, and RAM capacity. To quantify probabilities and verify cloud scaling objectives, we employ Probabilistic Computation Tree Logic (PCTL). Experimental evaluations were conducted to assess the performance of the formalized cloud scaling process. The results demonstrate that the non-deterministic scaling behaviors in MDP models effectively reduce extreme-provisioning events compared to DTMC, which lacks the non-determinism aspect. Moreover, the non-deterministic characteristic enables MDP models to exhibit varying levels of accuracy when tested with different sample sizes. In contrast, DTMC, which relies solely on probability-based state transitions, maintains its accuracy in capturing the scaling behavior regardless of sample sizes. Our contributions encompass a formalization approach for the cloud scaling process, considering both deterministic and non-deterministic scaling actions. We present experimental results comparing MDP-based and DTMC-based cloud scaling processes, along with model accuracy results based on CPU utilization, response time, and RAM capacity. By addressing gaps in the existing literature, our study offers valuable perspectives and insights into the analysis of the cloud scaling process.